In hydrostatically lubricated mechanisms consisting of a rotatable worm and a linearly movable worm-rack, the trapezoid section of the teeth hitherto used in mechanisms without hydrostatic lubrication has been retained. The half-angle of the flank, i.e. the angle formed by the flank of the tooth with the line of action to the axis of the worm is in the range of 15.degree. to 20.degree. in this case. With these relatively large half-angles there is the danger that the table bearing the rack will be vertically displaced by the force components bearing in a vertical direction on the flank, and this is especially liable to occur where the table rises in its guide. Moreover, as a result of the vertical displacement of the rack in relation to the worm, the space for lubrication between the flanks of the worm and the worm-rack is altered. With hydrostatic lubrication, this can lead to further disturbances and inaccuracies in working. In addition, with hydrostatic lubrication a large half-angle for the flank has the disadvantage that the axes of the worm and the worm-rack must be very accurately aligned. Even a slight displacement of the axis of the worm-rack in relation to the axis of the worm will lead, in fact, to a considerable increase in the space for lubrication, so that a considerably higher performance is required of the pumps supplying the lubricating oil under pressure to the lubricating oil bore-holes, a performance which is often not available. Displacement of the center and the angle between worm and worm-rack can, in particular, be expected to result in uneven spacing over the length of the flanks. This may interfere to a considerable extent with the building-up of a hydrostatic film of the pressure medium.
The problem of the invention is to create a worm and worm-rack with hydrostatic lubrication, especially for machine tools, in which vertical displacement of the worm-rack in relation to the worm is avoided and in which both parts can nevertheless still be assembled and disassembled by vertical movement, i.e. by movement at right-angles to the axis of the worm.
This is achieved, according to the invention, in that (1) the lead angle of the worm, i.e. the angle formed between a tangent to the pitch helix and a plane perpendicular to the axis of the worm, is in the range of 2.degree. to 10.degree. and (2) the half-angle of the flank (.alpha.), i.e. the angle formed between the flank of the tooth and the line of the action to the axis of the worm, is in the range of 6.degree. to 10.degree.. The lead angle is preferably in the range of 2.degree. to 5.degree. and the half-angle of the flank (.alpha.) should preferably be equal to 7.degree..